Basics of Coordinate Geometry — NDA Mathematics PYQs

Directions : For the next two (02) items that follow :
Let $X(a,p)$, $Y(b,q)$ and $Z(c,r)$ be the points such that a, b and c are in AP.

If p, q and r are in AP, then the points X, Y and Z are

Directions : For the next two (02) items that follow :
Let $X(a,p)$, $Y(b,q)$ and $Z(c,r)$ be the points such that a, b and c are in AP.

If p, q and r are not in AP and $b=c$, then the line joining the points X, Y and Z is parallel to

If $p$ and $q$ are real numbers between $0$ and $1$ such that the points $(p,1)$, $(1,q)$ and $(0,0)$ form an equilateral triangle, then what is $(p+q)$ equal to?

If the vertices $B$ and $D$ of a square $ABCD$ are $(2,3)$ and $(4,1)$ respectively, then what is the area of the square?

The number of points represented by the equation $x=5$ on the $xy$-plane is

ABC is a triangle with $A(3,5)$. The mid-points of sides $AB$, $AC$ are at $(-1,2)$, $(6,4)$ respectively. What are the coordinates of centroid of the triangle ABC ?

If $P(2,4)$, $Q(8,12)$, $R(10,14)$ and $S(x,y)$ are vertices of a parallelogram, then what is $(x+y)$ equal to?

The points $(-a,-b),(0,0),(a,b)$ and $(a^2,ab)$ are:

If the point $(x,y)$ is equidistant from the points $(2a,0)$ and $(0,3a)$ where $a>0$, then which one of the following is correct?

A parallelogram has three consecutive vertices $(-3,4)$, $(0,-4)$ and $(5,2)$. The fourth vertex is